1. Introduction
One of the main directions of development of the global engine building industry is the increase of technical & economic indicators and improvement of the environmental performance of the compression ignition and turbine engines. This paper is devoted to the physical modeling and mathematical simulation of the characteristics of complex convective and radiant heat exchange for the coated combustion chamber (CC) wall using the semitransparent or opaque thermal barrier (heat-insulating) materials (TBMs) and coatings (TBCs).
The authors aim to show the possibility of controlling thermal modes within subsurface zones and near CC wall using semitransparent materials (coatings) in comparison with traditional opaque heat-insulating ones. This ensures NOx emission reduction and heat loss control (determining engine efficiency) through the CC wall at the required level due to the formation of a lower subsurface temperature gradient (even at possible positive one grad [T(x = 0,t)] > 0 as a result of influence specific optical properties) and appearing the corresponding temperature maximum inside semitransparent media.
The used optical and thermal physical models of these materials depend on their selective structure causing volumetric reflection (absorption) and low heat conductivity due to variable porosity and foreign matter concentrations. Taking into account the semitransparent properties of the CC inner surface is relevant because in many studies a significant effect of radiation is shown in complex heat transfer studied over many decades. The need to consider complex heat transfer with a significant proportion of the radiant component in the CC power-plants operating at elevated temperatures was justified in many works of known scientists for diesel [
1,
2,
3,
4,
5], turbine engines [
5,
6,
7], power stations, vehicles, aero-engine parts, and in nuclear engineering [
8]. Here is the phrase of an American automotive engineer [
1], who clearly indicated already in 2019 the trend of research in the modern automotive industry: “… toward higher operating pressures and higher levels of exhaust-gas recirculation in compression-ignition engines, together with the demand for higher quantitative accuracy, has led to renewed interest in radiative transfer in engines.”
Many scientists confirm [
5,
6,
7,
8,
9,
10] the intensive development of TBMs (TBCs) by the global automotive and aerospace industries. Research for decreasing costs and consumed fuel in internal combustion engines and gas turbine have been continuing. Engine efficiency improvement efforts via constructional modifications are increased today; for instance, parallel to the development of advanced technology ceramics, ceramic coating applications in engines grow rapidly. But in many studies, ceramics were not considered in terms of their semitransparent properties. In the special issue of “Thermal Barrier Coatings” of journal “Coatings” in 2019 on the modern research trends, the presented articles also did not reflect the development of scattering (absorbing) materials and coatings [
11].
The authors have repeatedly noted in their previous works [
9,
10] in 2007–2017 that despite the legendary developments of CC walls coated by ceramic as a semitransparent substance in their current researches, this factor is not considered. This is strange because there are numerous developments of opaque and semitransparent heat-shield composites for aerospace vehicles of American and Soviet engineers [
12,
13,
14] since the 1960s.
So, in most current works, the optics of ceramic heat-insulating materials and coatings have not become the subject of research [
1,
3,
15,
16,
17,
18,
19]. Without knowledge optics of material, the empirical techniques for estimating radiant heat transfer parameters are still offered as the base engineering methods of calculation nowadays [
2,
3]. In the theoretical work [
16], a time-periodic model of coated CC thermal conduction changing has been used to calculate the wall temperature swings along the combustion chamber surface within an engine cycle. In other experimental work [
17], indirect experimental estimations of convective fluxes dynamics (by high-speed photo registration) are used to offer quality models of thermal modes for heat-insulating ceramic coatings of diesel CC walls. However, in these works, there is no mention of the radiant penetrating component of the total heat flux and the semitransparent properties of the exposed TBMs (TBCs). Instead, the partial absorption of total heat fluxes (without separation convective and radiation components) in the subsurface zone of exposed materials was modeled as an effect due to the influence of porosity [
18] without including the optical factor of the heat transfer analysis.
This is a repetition of the introduced famous semi-empirical Annand’s formulas [
2] and its modifications [
3], in which the separation of radiant fluxes by the wavelength spectrum was also absent. Thus, fundamental physical analysis of radiative-conductive heat transfer for ceramic heat insulation is being replaced by the development of different exotic models of subsurface heat conductivity and only surface reflection for all the spectral radiant components of total heat load [
16,
17,
18,
19].
Modeled optical characteristics of ceramic thermal insulation must be consistent in the spectrum with the penetrating radiant component, which reaches 50% in CC diesel [
2,
3] and 40% in CC gas turbine [
1,
5,
6,
7] engines. In Russia, theoretical studies have been carried out for simulation of the radiant fluxes (up to 1–2 MW/m
2) & emissivity for spectral radiation range 0.4–9 μm of red-hot soot particles causing the formation of a temperature field in the CC walls of different power plants [
20]. This radiation is close in its properties to Planck radiation and can be used for theoretical estimates of the absorbed energy function.
In this paper, the authors continue their theoretical and experimental researches on promising types of ceramics with heat insulation properties both for convective fluxes and thermal radiant ones of model CC walls using ceramics with optical and thermal physical parameters due to different porosity [
13,
21].
3. Results and Discussion
In accordance with the proposed optical models and other properties (See
Table 2), the heat conductivity Equation (6), (10) at
F(x) ≠ 0 for semitransparent TBM and opaque one (6) at
F(x) = 0) with appropriate nonlinear boundary conditions (7)–(9) were solved numerically for a single layer of flat plate for semitransparent (See
Figure 1a: I) and opaque (See
Figure 1b: II) ceramics under intensive radiant (See
Figure 1a,b: arrow 1-0) and convective (3I) heat fluxes with forced cooling (3II) on the CC walls back surface. The software was developed based on the universal languages Mathcad, Matlab.
Figure 2 presents: (a) thermal radiation fields of the absorbed energy per time and volume unit
F(x) under shortwave radiation flux; and (b) volumetric reflection
r(
x), transmittance
τ(
x) coefficients for a plane-parallel semitransparent sample (thickness 0.01 m) at the optical model M(
κ/σ−A) with albedo (
A, %), absorption (
κ, m
−1) and scattering (
σ, m
−1) indexes due to different porosity (See
Table 2). Model M
se3 (14/2400-86) is described by the optical characteristics obtained by the authors using the experimental lasers set up with integrating the photometric sphere sandblasted cast aluminum [
21].
The following optical models were used to calculate the radiant fields in semitransparent materials M(
κ/σ-
A): M
se1 (14/1000-79)—curves 1 (
Figure 2a,b); M
se2 (14/1500-83)—2; M
se3 (14/2400−86)—3 (experimentally investigated sample Y-PSZ); M
se4 (14/3000-87)—4; M
se5 (14/3500-88)—5, M
se6(28/1000−72)—6. With growth scattering of radiation, there is a decreasing absorption of penetrating radiation: from model M
se1 (
σ1 = 1000 m
−1) to M
se5 (
σ1 = 3500 m
−1). Absorption index increasing two times (up to
κ2 = 28 m
−1 - model M
se6) causes a sharp growth of the absorbed energy (
Figure 2a: curve 6) in the subsurface zone. Thus, the efficiency of scattering (volume reflection) processes will substantially depend on the absorption. That’s why the structuring of porous ceramics should be carried out based on chemically pure starting materials.
The calculated radiation fields show important features of semitransparent media: For a more uniform volumetric distribution of absorbed radiant energy, the materials must have small scattering and absorption. Maximum scattering ensures the most reflection and least transmittance for a layer with a given thickness (
Figure 2b: model M
se5—curves 5
r and 5
τ).
To obtain the calculated temperature fields, the nonlinear problem of radiant-conductive heat transfer within the semitransparent monolayer
H (CC wall) was solved using the technique developed by the authors of [
9,
10] and similar calculation-theoretical methods of other works [
5,
8] for model TBMs samples.
Figure 3 shows an example of simulated complex convective and radiant heating of CC thermal barrier ceramics under constant radiant heat loading ~0.9 MW/m
2; at a constant temperature 800 K of gas mixture; heat transfer coefficient α
T = 1500 W/m
2·K; emittance of gas atmosphere
ε1 ~0.4 and for exposed wall as black body 1 (in long-wave range) for ceramic single flat plates with a thickness
H =10 mm for time modes of external combine heat action:
- -
during t1 = 0.01 s and t2 = 0.1 s for diesel engine (a), and
- -
accordingly, for turbine engine CC walls at t3 = 10 s (b) and t4 = 100 s (c)
with convective cooling (αT = 200 W/m2·K) on the CC wall back surface.
The optical characteristics are presented in
Table 2 for semitransparent Y-PSZ samples (curves 1…6) with different optical models M
se(
κ/σ-A) and opaque (model polluted) samples M
op with surface reflection
R = 30%, large absorption and the same thermal characteristics (curves-7).
For a typical heat load inside combustion chamber of high-speed diesel, the use of a semitransparent material (optical model M
se3 [
21]) with scattering indices
σ = 2400 m
−1 at absorption index
κ = 14 m
−1 (See
Figure 3a, curve 3-
2) leads to a temperature decreasing by 30 K in surface temperature compared with the non-transparent, opaque one (model M
op7, curve 7-
2). The estimates obtained are in good agreement with the qualitative results in [
5] and are numerically close to the data in [
7]. In the last article, the semitransparent model shows a temperature reduction by 45 K for Y-PSZ of high volumetric reflectance (80%) compared to the same ceramics, but opaque one (for example, polluted by absorbed foreign substance) with low reflectance (20%).
The authors of work [
7] described only reflection coefficients without taking into account the influence of scattering and absorption. That’s why the advantages of highly reflective ceramics and the ability to control the thermal regime of TBM by changing its porosity (microstructure) were not considered. The presented semitransparent ceramics correspond to the models M
se2-M
se3 with porosity
P~9–18% (See
Table 2).
As in well-known work [
5], in
Figure 3b,c, for turbine CC, the subsurface temperature maximum begins to form at a depth of several millimeters with a stationary total heat load up to 2 MW/m
2 with a 50% fraction of the penetrating short-wave radiant component during prolonged heating for more than 10 s. In a semitransparent material, subsurface radiant overheating can cause a temperature maximum comparable in magnitude to the surface temperature of an opaque ceramic. A decrease in surface temperature during prolonged heating can reach hundreds of degrees (See
Figure 3b: curves 6-3 and 7-3;
Figure 3c: curves 3-4,…, 6-4 in contrast 7-4). Thus, the subsurface zone of the semitransparent material will cause radiant overheating and the accumulation of radiant energy part of the total heat flux due to the optimal selection of the optical models determined by the structure of TBM (TBC).
The interest for ceramic TBMs (TBCs) in particular is determined by the creation of a new class of semitransparent coatings capable of absorb and accumulating a radiant component of thermal flux in the near IR (~1 ÷ 3 μm) within subsurface volume during the combustion of a fuel blend in CC of diesel and turbine engines. Simultaneously, the long-wave radiant component (~3–5 μm) in the mid-IR range corresponds to a lower emission heat flux in comparison with the short-wave component one.
Engine makers did not take into account optical properties (near IR) of heat-insulating materials and coatings. That is why the traditionally radiant components of the heat flux have been considered as absorbed ones on the CC boundary internal surface as well as convective component.
At small heating times (for one full cycle of the piston’ movement in the diesel CC), high scattering causes a surface temperature decrease by 10–20 K at
t1 = 0.01 (See
Figure 3a, curves 3-
1 in comparison with 7-
1). For
t2 = 0.1, the temperature decreases up to 70 K (See
Figure 3a, curves 1-
2, ..., 4-
2 in comparison with 7-
2) due to volumetric radiant overheating. Curves 5-
1 and 5-
2 for a semitransparent material correspond to the thermal mode of an opaque TBM, but it represents an exotic variant for physical modeling and mathematic simulation of optical properties with little influence of thermal conductivity.
However, at large heating times, 3rd thermal mode
t3 = 10 s (when the influence of the thermal conductivity coefficient begins to appear), there is more extensive subsurface overheating during deceleration of the growth surface temperature and decreasing (in modulus) of the negative temperature gradient (See
Figure 2b: curves 1-
3,…, 6-
3). Under these thermal modes, the overheating of an opaque material surface exceeds by 200 K (curves 7-
3) the temperature within the thickness of a semitransparent TBM (curves 1-
3,…, 6-
3). Of course, this level of overheating is unacceptable and this led to the use of semitransparent oxides even without any theoretical justification.
A subsurface temperature maximum forms in ceramics at long periods of fuel combustion for hot sections of a gas turbine engine, for example, at 4th thermal mode
t4 = 100 s (See
Figure 3c: curves 1-
4,…, 6-
4). In this physical model, the influence of the thermal conductivity coefficient begins to prevail (in comparison with scattering), and the subsurface overheating zone increases with constant adsorption index. The scattering index (over a wide range of its changes) can be modeled by the microstructure (porosity) for control thermal modes under penetrating intensive thermal short-wave radiation.
The intense intrinsic reradiation of the exposed ceramic surface in the long-wavelength region of the spectrum with a high black factor also stimulates internal overheating by short-wave radiation.
Also, simulation results show that, in such media, not forming surface temperature, but a generated subsurface maximum could be used to ensure optimal thermal modes under intensive short-wave infrared radiation. Internal walls do not achieve these extreme temperatures using semitransparent materials (coatings). This allows us to decrease surface temperature for the internal surface combustion chamber and to limit the formation of toxic nitrogen oxides.
Thus, the generation and emission of nitrogen oxides NOx could be controlled caused by the management of radiant overheating inside semitransparent heat-insulation in which surface temperature is decreasing due to volumetric radiant absorption. It was shown that the subsurface radiation and temperature fields are determined first of all by optical characteristics, which can be modeled using the selected microstructural porosity of ceramic thermal insulation.
For these cases, the required porosity of ceramics can be limited by P ~15%. The selective shape and size of pores (or scattering particles) can become a technological parameter that determines the optical model with varying scattering and absorption characteristics at constant porosity. The value of the heat conductivity coefficient will not change significantly.
The presented methodology for modeling and control of subsurface radiant and temperature fields in semitransparent scattering and absorbing ceramic materials may be the basis for studying the thermal modes under pulsed and periodic exposure. Suggested models of physical and mathematical modeling will be needed when creating heat-insulating materials and coatings in various fields of science and technology, in the automotive and aerospace industry, shipbuilding, etc.
4. Conclusions
The structural ceramics presented (as ceramic thermal insulation) differ in their thermal modes of heat transfer: with a conductive (silicon carbide and silicon nitride) mechanism and radiation-conductive (metal and silicon oxides) one (See
Table 1 and
Table 2). Thus, with the generated intense radiant component in CC, semitransparent oxides become the more preferred TBM in contrast to the opaque one.
The structural composition of the semitransparent ceramics ZrO
2 (Y-PSZ), Al
2O
3, and SiO
2 can ensure the necessary scattering and absorption to control the temperature profile in the exposed ceramic wall. However, with approximately the same effect of optics on heat transfer through the ceramic wall, the linear expansion factor becomes a determining parameter, because it is the closest in terms of this coefficient to metal substrates. Due to its high linear expansion factor coefficient ZrO
2 stabilized by 5–20% Y
2O
3 is most widely used for the production of ceramic coatings with operating temperatures up to 2500 K. Moreover, the crack resistance and stress limit characteristics for other ceramics are close to each other (See
Table 1).
Also, among the many materials, zirconia has a unique upper bound of the spectral transparency window. Thus, it can be confidently stated that the full radiant flux of red-hot soot particles will be absorbed in the subsurface zone and not on the exposed surface of ceramic heat insulation.
Reduced scattering leads to greater transparency of the irradiated medium and absorption in a wider subsurface zone. Of course, with low absorption, i.e. in the absence of absorbing impurities. Thus, the production of heat-resistant semitransparent ceramics requires an initial powder in a high degree of purity up to 96–99%.
Convective fluxes growth (at lowering of the exposed surface temperature) also stimulates subsurface overheating with a positive temperature gradient. A decrease in the temperature of the gas atmosphere and the inner surface of the CC walls will contribute to the sink of conductive heat to the exposed surface from the overheated subsurface zone.
The subsurface overheating effect is observed both in semitransparent materials and in translucent natural environments, for example, in snow and water covers [
28,
29].
The authors believe that the use of modern methods for the manufacture of ceramic materials and coatings can ensure the construction and build-up of the required microstructure of TBMs or TBCs for optimal conditions of the thermal mode selection under the influence of a powerful radiant convective load.
The next generation of green and efficient vehicle power-plants will be determined by the rapidly growing development of advanced technology of semitransparent ceramics allowing to optimize its thermal modes.
Commercial value releases zirconium oxides as the most expensive material (See
Table 1). However, this is not an obstacle, given the benefits of using new types of semitransparent TBM (TBC) to create heat-resistant parts for hot sections of gas turbines and piston heads of diesel engines.